I unzipped the ShowUI module
to:C:\Users\Tony\Documents\WindowsPowerShell\Modules

After unzipping it shows a folder inside the Modules folder of ShowUI and
inside the ShowUI folder there are two files ([Content_Types].xml,
install.cmd) and another ShowUI folder. Inside the second ShowUI
folder there are numerous other files and folders.

When I open the PowerShell ISE version 6.3.9600,16384 from
C:\Windows\System32\WindowsPowerShell\v1.0 and run “Import-Module
ShowUI” from the prompt, I get this error:

“Import-Module
: The specified module 'ShowUI' was not loaded because no valid
module file was found in any module directory.
At line:1 char:1
+
Import-Module ShowUI

When I use the $PSVersionTable, I get the following
information:
Name Value
PSVersion 4.0
WSManStackVersion 3.0
SerializationVersion 1.1.0.1
CLRVersion 4.0.30319.34003
BuildVersion 6.3.9600.16394
PSCompatibleVersions {1.0, 2.0, 3.0,4.0}
PSRemotingProtocolVersion 2.2

The "[Content_Types].xml" file sounds like a NuGet/Chocolatey package thing, is someone distributing it like that? In any case, it sounds like you need to move up the inner module folder.

From what you said, it sounds like you have an extra ShowUI folder, something like: C:\Users\Tony\Documents\WindowsPowerShell\Modules\ShowUI\ShowUI\ShowUI.psd1

When a PowerShell module is properly installed you should have a MODULENAME.psd1 file inside a MODULENAME folder ... inside a folder that is in your
$Env:PSModulePath

So for instance:

If you type: $Env:PSModulePath -split ";"

One of the lines should be C:\Users\Tony\Documents\WindowsPowerShell\Modules\

In that Modules\ folder you want one folder named ShowUI

in that Modules\ShowUI folder you want to see ShowUI.psd1

That is, it should be: C:\Users\Tony\Documents\WindowsPowerShell\Modules\ShowUI\ShowUI.psd1

P.S. There doesn't technically have to be a .psd1 file (the best modules will all have .psd1 files, but) it could be
just a .dll or .psm1 or .cdxml file ... but it still has to have the same name as the folder, and it shouldn't be nested in further subfolders.

I downloaded ShowUI from your link and it gave me the same file and folder structure as I originally explained.

I copied the second ShowUI folder and its contents to the Modules folder so it looks like this:
C:\Windows\System32\WindowsPowerShell\v1.0\Modules\ShowUI

When I use this cmdlet: Import-Module ShowUI, it gave this error:
PS C:\Program Files\Microsoft Office\Office14> Import-Module ShowUI
“Import-Module : File C:\Windows\system32\WindowsPowerShell\v1.0\Modules\ShowUI\Get-ReferencedCommand.ps1 cannot be loaded because the execution of scripts is disabled on this system. Please see "get-help about_signing" for more details.
At line:1 char:14

Using the information from the get-help about_signing cmdlet, I used this cmdlet: set-executionpolicy remotesigned and it yielded this:
“PS C:\Program Files\Microsoft Office\Office14> get-executionpolicy
RemoteSigned”

Again using the information from the get-help about_signing cmdlet, I followed this:
To run an unsigned script:

I also followed the instructions to CREATE A SELF-SIGNED CERTIFICATE and to SIGN A SCRIPT, getting this result:
“PS C:\Program Files\Microsoft Office\Office14> Set-AuthenticodeSignature C:\Windows\System32\WindowsPowerShell\v1.0\Modules\ShowUI\ShowUI.psd1 $cert

Yet when I run the Import-Module ShowUI, I get this error:
“Import-Module : There were errors in loading the format data file:
Microsoft.PowerShell, C:\Windows\system32\WindowsPowerShell\v1.0\Modules\ShowUI\ShowUI.Formats.ps1xml : File skipped because it was already present from "Microsoft.PowerShell".
Microsoft.PowerShell, C:\Windows\system32\WindowsPowerShell\v1.0\Modules\ShowUI\ShowUI.Formats.ps1xml : File skipped because it was already present from "Microsoft.PowerShell".
At line:1 char:14

Then ran this again: Import-Module ShowUI and got this result:
Import-Module : There were errors in loading the format data file:
Microsoft.PowerShell, C:\Windows\system32\WindowsPowerShell\v1.0\Modules\ShowUI\ShowUI.Formats.ps1xml : File skipped because it was already present from "Microsoft.PowerShell".
Microsoft.PowerShell, C:\Windows\system32\WindowsPowerShell\v1.0\Modules\ShowUI\ShowUI.Formats.ps1xml : File skipped because it was already present from "Microsoft.PowerShell".
Microsoft.PowerShell, C:\Windows\system32\WindowsPowerShell\v1.0\Modules\ShowUI\ShowUI.Formats.ps1xml : File skipped because it was already present from "Microsoft.PowerShell".
At line:1 char:14

You don't need to mess with code-signing unless you're in a corporate environment where it's required, just run PowerShell "As Administrator" once, and set the policyt to allow scripts to run:
Set-ExecutionPolicy RemoteSigned or even Set-ExecutionPolicy Unrestricted

The second error you got is a bug in PowerShell. When you ran Import-Module the first time, you got an error, but PowerShell partially imported the module ... once you fixed that error, when you tried again, you got errors indicating that it's not reloading
the format file, because it already loaded it. That's batty and buggy, but you can probably ignore it. Certainly if you open a new PowerShell window it should work fine.